Data transformation in biological assays

Abstract

The analysis of variance is the statistical test most used for comparison of three or more means simultaneously. Its application requires, however, the compliance to some assumptions, with main emphasis on normality of the data and homoscedasticity of variances. When such requirements are not met, one of the alternatives is the data transformation to enable the continuity of the experimental evaluation. With the proposition of the Tukey’s data transformation system, understood as a power transformation system, i.e. the application of nth root on a data set (X⅟n) this statistical procedure has methodologically evolved to ensure such solutions. In the present research we proposed a complement to this system, denominated here as transformation in four steps, with inclusion of two hypothesis tests to evaluate normality and homoscedasticity. This was applied on experimental data to evaluate the amount of radiation available at soil level within stands of Acacia mearnsii De Wild. We have proposed a model for data transformation to simultaneously obtain homoscedasticity and normality. The methodology was appropriate to ensure these two statistical aspects on the experimental data, allowing comparison of eight treatments by conventional analysis of variance. Index terms: Analysis of variance, homoscedasticity, normality.